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受欢迎的代数 >

4x^2-2(a^2+b^2)x+a^2b^2=0

解答

4 x^{2} - 2 (a^{2} + b^{2}) x + a^{2} b^{2} = 0

解答

x = \frac{a ^{2}}{2}, x = \frac{b ^{2}}{2}

求解步骤

4 x^{2} - 2 (a^{2} + b^{2}) x + a^{2} b^{2} = 0

展开

4 x^{2} - 2 (a^{2} + b^{2}) x + a^{2} b^{2} : 4 x^{2} - 2 a^{2} x - 2 b^{2} x + a^{2} b^{2}

4 x^{2} - 2 a^{2} x - 2 b^{2} x + a^{2} b^{2} = 0

改写成标准形式

a x^{2} + b x + c = 0

4 x^{2} - (2 a^{2} + 2 b^{2}) x + a^{2} b^{2} = 0

使用求根公式求解

x_{1, 2} = \frac{- ( - 2 a ^{2} - 2 b ^{2} ) \pm ( - 2 a ^{2} - 2 b ^{2} ) ^{2} - 4 \cdot 4 a ^{2} b ^{2}}{2 \cdot 4}

化简

(- 2 a^{2} - 2 b^{2})^{2} - 4 \cdot 4 a^{2} b^{2} : 2 (a + b) (a - b)

x_{1, 2} = \frac{- ( - 2 a ^{2} - 2 b ^{2} ) \pm 2 ( a + b ) ( a - b )}{2 \cdot 4}

将解分隔开

x_{1} = \frac{- ( - 2 a ^{2} - 2 b ^{2} ) + 2 ( a + b ) ( a - b )}{2 \cdot 4}, x_{2} = \frac{- ( - 2 a ^{2} - 2 b ^{2} ) - 2 ( a + b ) ( a - b )}{2 \cdot 4}

x = \frac{- ( - 2 a ^{2} - 2 b ^{2} ) + 2 ( a + b ) ( a - b )}{2 \cdot 4} : \frac{a ^{2}}{2}

x = \frac{- ( - 2 a ^{2} - 2 b ^{2} ) - 2 ( a + b ) ( a - b )}{2 \cdot 4} : \frac{b ^{2}}{2}

二次方程组的解是:

x = \frac{a ^{2}}{2}, x = \frac{b ^{2}}{2}

作图

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